Solar System Formation: Haphazard Accumulation? No! Now that we have explored it is time to ask again about its possible origins, first by considering -- and quickly dismissing -- the notion of haphazard accumulation. First, of course, I must explain what I mean by this expression! I am asking you to visualise the sun itself forming in splendid isolation, in the middle of empty space. Later, it might somehow capture chunks of rock and other material as they come sailing by on their way through space, and thus build up a retinue of planets. Of course, such a 'model' does not provide any explanation of how the sun or the planets actually formed as individual objects! The working assumption is that those origins were completely independent, both in space (they may have formed in different locations) and in time (they may have formed at very different times in the past). Is it not possible, for instance, that the Earth formed four billion years ago, but that Jupiter was formed, say, two billion years ago, and was captured by the sun a mere three hundred million years ago? How could we hope to test this? As it happens, I don't have to dream up elaborate tests of such a theory because we can instantly rule it out on various grounds, as follows: Objection 1: There is no plausible mechanism whereby this could happen. If the sun were sitting alone in space, and a chunk of rock (the early Earth?) approached it from a long way away, the rock would speed up under the pull of the Sun's gravity and would fall faster and faster towards it. By the time it was close to the sun, it would be moving very quickly, and would have enough energy to fly off into space again. (Remember the conservation of energy! Gravitational potential energy is converted to kinetic energy -- the energy of motion -- but then cannot merely disappear.) An analogy may help. If you watch a child on a swing, when she is at the top of the backswing, she is momentarily at rest. As the swing starts to fall under the influence of gravity (with the ropes constraining it to move in a forward direction) it picks up speed until it is moving very quickly at the bottom of the swing. It then has enough energy to climb up about as high as it was when it started. Unless there is some sudden dissipation of energy near the bottom (like you blocking the swing's motion), it will not simply come to rest there. Of course, air resistance does provide a continuous resistance and loss of energy, so a swing, unless pumped or pushed, will eventually come to rest. But this does not affect infalling rocks or planets near the sun: there is no appreciable air resistance or other loss of energy. Indeed, for this reason a rocket approaching the moon has to fire its rockets to slow down if it wants to go into orbit. The moon will not simply obligingly `capture' it! In the early solar system, the only way that a rock or planet falling towards the sun could be slowed down and go into orbit around it would be if it collided with some material which was already there and got slowed down just the right amount. As you will agree, it is not very likely for this sort of thing to have happened nine times, each time happening so precisely that the chunks wind up in near-perfect circular orbits! Moreover, one would not expect the planets which accumulated this way, one at a time, to all be in the same plane, all orbiting the same way, and so on. (Presumably they would have arrived from various directions.) Objection 2: The second objection follows the same sort of reasoning. If the planets were captured haphazardly, there is no mechanism which would make the small rocky chunks wind up near the sun and the bigger gaseous ones farther out. Do not make the mistake of assuming that the denser rocky objects will settle closer to the sun! That happens only if the objects are in a buoyant medium. Let us explore this further, since it is a very common mistake. First, think about our everyday Earth-bound experience. When you are at the lakeshore, for instance, you will notice that stones plunge to the bottom of the lake; silt settles slowly through the water; people float with a bit of them sticking out of the water; an air-filled beach ball floats almost entirely "on top" of the water; and a helium-filled balloon is buoyed up by the atmosphere and rises into the sky. By contrast, however, the planets are moving through the near-perfect vacuum of empty space, and feel absolutely no buoyancy. They can be in any orbit they like, depending on their speed and regardless of their masses. As I noted before, in introducing the a feather and a truckload of scrap iron could be placed into identical orbits around the sun and would stay there. In fact, if we had inexhaustible power supplies, we could in principle move the Earth itself into a new orbit far away from the sun. It would not then 'settle back' towards the sun because of its density, but would instead orbit out there perfectly happily forever. Now, given these two strong objections, you may wonder what the positive aspects of the hypothesis of haphazard accumulation are. The answer is that there are none, and the model simply cannot be correct! It is apparent that the sun and the planets must all have formed at about the same time, in some process which produced the striking regularities which we noted earlier. We must therefore consider the merits and deficiencies of the other two possibilities.

A Catastrophic Origin?

The central idea in this hypothesis is the dramatic one of a near-collision between two stars moving independently in space, one of them being the sun. If they came very close to each other, this would result in streamers of material being pulled off by their mutual gravitational influences - that is, by tidal forces. After the stars went on their independent ways, the material in the streamer swirling around the sun might then condense into the 'blobs' which we now call the planets. This hypothesis, which was very popular about a century ago, has some immediately appealing aspects, but also some fatal flaws, as we will see. Appealing aspect #1: understanding the systematic motions. If you imagine one star skimming past the other, you will probably agree intuitively with the suggestion that any drawn-off streamer of material would wind up moving in the same sense. The result would probably be a streamer of hot gas swirling around the sun in the well-defined direction of the near-miss. It would presumably also be somewhat drawn out (or flattened) in the plane in which the two stars are moving. This qualitative consideration would seem naturally to explain why the planets move in the same direction and in the same plane! (It is not, however, so successful in explaining why the orbits should be nearly circular.) Appealing aspect #2: the sizes of the planets. When this model was in vogue, it was argued that the streamer pulled off would be shaped somewhat like a very long skinny football, as least to begin with. This might explain why Jupiter is so big (since it forms near the fatter central part of the streamer) and the planets at either extreme are smaller. So much for the positive side. There are, however, some strong objections as well: Fatal flaw #1: the failure to form planets. Unfortunately, it is fairly easy to show (with a modern understanding of the relevant physics) that any streamer of gas pulled off the surface of the sun would be much too hot to condense into planets: the atoms would simple "boil off" into the vacuum of space, and no planets would be formed. This is so dramatically the case that it completely dooms the model in its original form. (It is perhaps worth noting that a revised version of this model is still receiving some support. If a near-collision happened when the sun was not yet quite a star, but still a somewhat distended ball of cool gas, then any streamer pulled out might in fact condense to form planets. That revised model has other problems, however, so the case is still not very strong.) Fatal flaw #2: the distribution of angular momentum. A second problem, a little less simple to grasp, is that a near-collision like this cannot explain how it is that the planets have so much of the angular momentum in the solar system. Let me explain. As you will remember, is a measure of the amount of spinning (orbital and/or rotational) motion in a body or a system of bodies. In the solar system, the sun is more or less at rest in the centre, and is rotating only very slowly (once every 25 days); thus it has very little angular momentum. Jupiter, on the other hand, is quite a big object and is spinning rapidly (once every ten hours). In addition, it is orbiting around the sun, moving in a big nearly-circular orbit. The net result is that it has a lot of angular momentum, and indeed the planets taken all together have about 99 percent of the angular momentum in the solar system. If you believe in the catastrophic origin, it is very hard to explain this. How could the near-collision have pulled a streamer off the sun in such a way that the material is set spinning and orbiting, while at the same time leaving the sun scarcely turning at all? Here is an analogy to make the problem more obvious. If you were spinning on a piano stool, you could slow down your spin by throwing a heavy object away from you in the forward direction. (It 'carries away' some of the total angular momentum, leaving you rotating less quickly.) But you can see that it would be remarkably coincidental if you threw the object at precisely the right velocity to bring yourself more-or-less to a perfect stop. And yet that is (almost) what has happened in the solar system. The collision hypothesis has real trouble explaining that.

A Profound Implication: Our Uniqueness.

As I noted, the catastrophic (or collision) hypothesis was once quite popular. If indeed it had been correct -- which now seems very unlikely -- it would have had an important and humbling implication, as follows: The profound implication: our uniqueness. If the catastrophic hypothesis is correct, then there are probably at most only a handful of solar systems in the whole Milky Way galaxy, and perhaps only one, even though the Milky Way contains about one hundred billion stars. The reason for this is quite simple. The stars are so widely separated, and moving at such modest speeds, that the chance of near-collisions between any two of them are vanishingly small. During the entire age of the galaxy, we might by chance expect only a couple of such encounters. If this is how planetary systems form, they must be very rare indeed! This implication has a corollary: if we look at some nearby stars and discover that they have planets, then the catastrophic hypothesis must be wrong. Why? It is because of the fact that, if such catastrophes have happened only rarely, then the tiny number of solar systems produced in this way must, on average, be very far apart. We would not expect to see another one anywhere near us in the galaxy! To convince you of what I am saying, permit me to offer a simple analogy (although it's perhaps a little far-fetched). Suppose you have always been a total recluse and have had absolutely no close contact with any other people. By glancing out the window at the occasional passer-by, you gain a knowledge of some of the more obvious attributes of average human beings (their heights, their hair colour, ...) but you can't see fine details like eye colour. Of course, your isolation doesn't prevent you studying yourself in considerable detail. You discover that your eyes are blue, and for some reason, you become persuaded that this is the result of some extremely improbable accident of birth. (Naively and imaginatively, let us say, you persuade yourself that your blue eyes were the result of a powerful nearby lightning strike happening during a total eclipse of the sun just at the moment of your birth.) Logically, you conclude that blue-eyed people are so very special and rare that there may be only one or two on the whole planet Earth. Suddenly you become more outgoing, and start visiting your fellow human beings in the neighbourhood. To your surprise, you discover that your immediate neighbour has blue eyes, although he is not your age and has only recently moved into the neighbourhood (he was born somewhere else). It is time to reconsider your hypothesis! Otherwise you are forced to conclude that by incredible coincidence the one other living example of such a person happens to live right next door to you, having moved here long after he too was born under the immediate influence of an independent lightning strike during some other eclipse! You might desperately try to hang on to the theory, but if you then go on to discover that several of your neighbours have blue eyes, it becomes utterly untenable. Instead, it is overwhelmingly clear that your blue eyes are not the product of some very unusual episode at birth, but rather quite commonplace. The analogy is a pretty good one, in several ways: Historically, we have studied the stars in as many ways as possible, and thus have determined many of their general properties (analogous to the height and hair-colour of a passer-by). Detecting whether or not a particular star has a planetary system is much more difficult and challenging, although of course we obviously already knew that we ourselves live in such a system. We have only just developed the technology to allow us to determine that for the nearby stars. (Analogously, we can at last determine 'the colour of their eyes.') The stars near us now were not always in our vicinity, because stars move at random through space. Billions of years ago, the stars which are now in the 'solar neighbourhood' were extremely far away, and whatever local conditions affected or caused the formation of our system of planets along with the sun will not have had any influence on them. Stars are not all the same age, so they did not all form at the same time. (In Physics 016, we will learn how stellar ages are determined.) This is analogous to the fact that your neighbours have different ages, and reminds you that any common characteristics which they may share cannot have been imposed by some extremely unusual event unless it was improbably and independently repeated at the time of each birth. In short, if we discover planets around even a few of the nearest stars then the catastrophic hypothesis is surely dead, and we will need to seek a hypothesis in which planets are routinely formed in whatever event gives rise to the birth of stars. One last very important point: we needed to find other planetary systems to settle the issue. Some students seem to think that the collision hypothesis for the origin of the solar system could have been ruled out right off the bat because it is so improbable for stars to come close enough together to form planets. In effect, they are saying that we are unlikely to be in such a privileged and rare location. This is simply not logical! The improbability of collisions makes it unlikely that many systems exist, but it does not rule out the existence of one . If we admit that one solar system might have formed in this way, there's no reason to be surprised that we find ourselves in it. After all, where else could we ever have come into existence? As noted earlier, it is only in the last few years that we have established definitive proof of the existence of planets around other stars. Those observations, coupled with our lingering doubts about the physical mechanisms, really provide the crucial evidence that the catastrophic origin simply cannot be correct.

The Nebular Hypothesis.

Given the strikes against the notion of haphazard accumulation and the catastrophic hypothesis, we really need to find some other theory. The nebular hypothesis suggests that the solar system formed over a relatively brief span of time and all as a unit (sun, planets, and so on), from a nebula, or cloud, of interstellar gas (the Latin word `nebula' means `cloud'). Although there had been philosophical musings by others, the original idea, at least in a really scientific version, arose with the French scientist Laplace, about 200 years ago. There is quite a good summary of this model in Chapter 9 of the text, which you should read with due attention; I will not repeat all that discussion here, although I will highlight certain aspects below. I should perhaps warn you, however, that the figures shown on pages 229 and 241 are quite misleading. What you have to realize is that an enormous (but very low-density) gas cloud, spread out over a very large volume of space, contracted under its self-gravity (i.e. all the particles were attracted together by the cumulative gravitational effects of all the other particles in the cloud). The figure makes it appear as though a cloud merely flattens out but is otherwise about the same size, which is quite incorrect. There was a pronounced shrinkage of the original cloud, as well as a flattening out. Indeed, the original cloud might have been a light-year or so across: ten trillion kilometers. The Solar System, out to the orbit of Pluto, is about ten billion kilometers in diameter, a factor of a thousand less. Since the volume of the cloud is given by volume = length x width x height, the original cloud occupied one billion times as much space as the Solar System now does, so you can see that the gas was very thin to begin with - with perhaps only a few thousand atoms in every cubic centimeter. The air in the lecture room contains about ten million trillion atoms per cubic centimeter! So the gas cloud out of which the Solar System eventually formed was pretty nearly empty space, by everyday standards.

What Starts the Collapse?

The textbook does not discuss one important aspect in detail. You may have concluded from what I have been describing that any gas cloud sitting out in space will spontaneously collapse under its self-gravity and perhaps produce a solar system. But we see lots of gas clouds out in space now. (See the pictures on pages 227 and 230.) Why have they not all long since turned into stars and planets? Why is any gas left between the stars? The answer lies in the same sort of physics which applies to the atmosphere of the Earth. How is it that we can breathe at all when we are up on a mountain? Under the influence of gravity, why don't the molecules of the air all fall down to the ground and collect in a thin, dense layer there? The reason, of course, is that the the molecules are moving around at random with some vigour -- indeed, it is an indirect determination of this random motion which provides our usual measurement of temperature. Collisions between the particles provide a sustaining pressure which keeps the atmosphere 'puffed up.' Any downward-moving molecule is likely to bump into one moving upwards, and get bounced back higher into the air. So too in interstellar space. The cloud of gas has some internal energy (meaning that the particles within it are whizzing about), so there is a pressure which sustains it against the tendency of gravity to make it start to collapse. Why, then, do clouds ever collapse at all? Why do any solar systems form? There are two obvious ways this can happen. Cloud cooling: If the cloud were to lose some of its energy (most probably by radiating it away as electromagnetic radiation, in exactly the way that a hot coal radiates away energy as infrared radiation), then the gas might get cool enough to start collapsing. That is, the loss of energy means that the particles are moving more slowly, and gravity can pull them together more efficiently since the sustaining pressure has been decreased. In similar fashion, if we were to drastically cool the air in a sealed room, it would settle lower to the floor. Eventually, if the room gets cool enough, the molecules can stick together because the collisions between molecules are no longer vigorous enough to break the electrical bonds which hold them together. The gas then condenses into droplets and pools of liquid nitrogen, oxygen, etc. If it is colder still, the material can freeze into a regular crystalline structure: ice of various kinds will form. (You are perhaps familiar with dry ice, which is frozen carbon dioxide.) Once it gets started, the collapse tends to accelerate, going faster and faster. The gravitational forces become even stronger as the particles get closer together (remember how the force of gravity depends on distance!), and this speeds things up. You might wonder, then, why the collapse ever stops. Why don't all the particles collapse tightly together into a microscopically tiny volume and form a `black hole' or some very dense body? Here is why this does not happen: 1 To begin with, the big cloud cools off a little bit, and the atoms start to draw closer together under gravity. This process accelerates, and the collapse proceeds faster and faster. 2 As the particles get closer together, they collide more and more frequently, and some of the inward motion is converted to random jostling about. The particles wind up moving with higher random velocities, at least temporarily. This is just another way of saying that the temperature increases again, at least to some extent. The net increase may be shortlived, however, because much of the heat which is generated simply gets radiated out into space, leaving the cloud scarcely any warmer than it was. (You are all familiar with the fact that a hot body radiates energy. A space heater is an example.) The collapse continues. 3 In this way, the cloud contracts while there is a continuous cycling of potential energy into kinetic energy, then into thermal energy (random motions), and finally into radiant energy which escapes to the vacuum of space. The cloud becomes smaller and denser, but its internal temperature is not much changed. (The technical term is that the collapse is isothermal.) 4 Eventually, though, the particles get so densely packed that the heat can no longer escape. (Again, the technical terms is that the cloud becomes 'optically thick,' which merely means that radiation will not readily pass through it.) Any radiation which is emitted from the hot central regions gets blocked by the surrounding dense layers of matter, rather than escaping into empty space. The heat is trapped, and builds up. At this stage, therefore, the particles near the centre wind up moving with very high speeds (i.e. the gas is very hot), which means that they can provide enough sustaining pressure to stop any further collapse. 5 Although we will not see the details until Physics 016, the great heat of the gas now means that thermonuclear reactions can take place. This releases yet more energy, and a star is born. The critical thing to note is that the centre of the star becomes very hot merely because of the conversion of its original gravitational potential energy (when the atoms were all spread out in a low-density cloud) to the random rapid motions of the atoms and particles which fell together and collided. You don't need to invoke or understand nuclear reactions or any complex physics to understand why stars are hot. They get that way just by the mechanism of formation. The thermonuclear reactions then serve to keep the star hot and (as we will see later) extend its potential lifetime enormously. Cloud compression: How else might a gas cloud start to collapse? Well, a second possibility is that the cloud may be compressed a little, perhaps `pushed in' on one side, so that the atoms are closer together than they were. This of course makes the gravitational force that much more effective, and the collapse can take over, even if there is no dramatic cooling to start with. After this, the process continues just as described above. What could cause such a compression? Interestingly, it has been suggested that it might come from the shock wave caused when a nearby massive star ends its life in a supernova explosion (which we will learn about in Physics 016). The blast of material coming out from the supernova hits the nearby cloud and compresses it enough to start a collapse, leading to the eventual formation of a new star. In this way, the death of one star can result in the formation of another (or possibly more than one). There is some evidence from the composition of meteors that at the time the solar system formed, about , there was indeed a nearby supernova which showered the gas cloud with tell-tale high energy particles created in the energetic explosion.

Cloud Flattening.

Whatever starts the collapse (cloud cooling or slight compression), we have also to understand why we wind up with a flattened solar system. The distended cloud with which we begin is a large amorphous blob in space, with no particular shape to it. Why does the solar system wind up as flat as a pizza? The answer comes down again to our old friend the It seems very improbable that the original cloud would, just by coincidence, have absolutely no trace of net rotation or swirling motion within it. Instead, there will be some (perhaps very slight) circulation or motion of gas inside it. (Some atoms are moving one way, and some another, but when all these motions are added up, there is likely to be some slight cumulative motion in some random direction. This defines the `sense of rotation' of the cloud.) Given this slight original rotation, it is inevitable that the cloud will spin faster and faster as it contracts, preserving the sense of rotation, just as the figure skater speeds up in a spin by pulling his or her arms in closer to the axis of the spin. (See page 138 of the text.) The increasingly rapid spin leads to its flattening out. (If it helps, visualise a piece of whirling pizza dough thrown into the air, and examine the figure on page 229.) If you are still not sure that you understand this, look back at our discussion of As I explained, the total angular momentum of an isolated system (i.e. one not being acted upon by some outside forces) does not change. We used this to understand why a planet moves faster when it is nearer the sun: its `sideways motion' speeds up. (Mathematically, we noted that the product of the `sideways motion' and the planet's distance from the sun had to yield the same value at all times. Thus, if one of those quantities decreases, the other has to increase.) Here, the same reasoning applies. Granted, we have a cloud of many trillions of atoms, molecules and small grains rather than just a handful of planets; but the same physical laws still rule. As the atoms move in closer to the centre, under the influence of gravity, any `sideways' motion they have must increase in speed so that their angular momentum is conserved. (Since there are collisions between particles, some of the angular momentum of one particle can be shifted to another -- one particle slows down in a collision, while another bounces off with higher speed -- but the total angular momentum of the cloud is conserved.) Since the cloud began as something quite enormous, and shrinks by a huge factor, it speeds up in its rotation to quite an extent. The result of this rapid spinning is that the cloud flattens out, just as a spinning piece of pizza dough flattens out into its familiar pie shape. We can now understand why the solar system is flat, and why the planets all move in the same direction as they orbit the sun. It arises as a simple consequence of the fact that they formed out of a system in which there was a predetermined sense of rotation imposed by some small swirling in the original cloud. (It is no accident that the planets all obey the same traffic rules!) But we still have to develop an understanding of why we see a range of physical properties among the planets, and why a planet's individual nature is so dependent on its location.

Condensation Mechanisms.

How does the flattened swirling system of gas and dust grains turn into planets, and why do the planets differ in their compositional properties in the ways we have learned? Here I will describe the presently accepted model. You should not be surprised to learn that the details of this complex process are not completely understood, but there is broad agreement on much of it. There are two important factors to consider: 1 the presence of a temperature gradient; and 2 the absence of a compositional gradient. Let us consider those in turn. 1 The temperature gradient: The central blob of material (the newly-formed sun) became quite hot early in the formation process, for the reasons I have just outlined in the previous section. But would the whole nebula have become hot? The answer is no; the outer parts of it would have been fairly cool. Why? The answer is quite straightforward. Compared to the atoms that ended up in the 'proto-sun,' the atoms in the outer parts of the flattened nebula did not fall in as close to the centre. Consequently, less of their potential energy was converted to kinetic energy (the energy of fast motions), and the collisions between the particles was not as vigorous as right at the center. Result: reduced heating. There is a second consideration which becomes more important a bit later on. Once the hot sun forms, it will be radiating away its heat in the form of light, both visible and infrared. That will help to maintain a raised temperature in the other parts of the solar system (just as it still does today: the sun keep's us warm!) but of course those effects are reduced the farther out in the solar system you are. The net result of all this is that the solar nebula will have a pronounced temperature gradient , with the innermost parts being considerably hotter than the outer regions. 2 The absence of a compostional gradient: Consider first the distended interstellar gas cloud from which the solar system nebula will form. The gas in interstellar space does not generally have pronounced compositional variations from place to place: instead, it is 'all mixed up.' (You can think of the thin gas which fills the space between the stars as being uniformly chocolate everywhere rather than 'chocolate ripple.') In any randomly selected big scoop of such gas, you will find that about 2/3 of it is Hydrogen, about 1/3 is Helium, and that there are traces (a few percent at most) of other heavier elements whose proportions don't vary much from place to place. So the nebula had pretty much the same composition everywhere before the slow collapse into a disk. You may be surprised, however, to learn that the collapse itself does not introduce any compositional stratification. You probably visualise the rare, denser atoms (like gold and iron) falling in farther to the centre, and the light atoms (like hydrogen) winding up farther our. But once again you have to remember that the atoms and particles fall inwards in exactly the same fashion under the influence of gravity! (Remember the Principle of Equivalence, and reconsider what I said above about the absence of any buoyancy. The heavier atoms, like iron, would not have fallen any faster towards the proto-sun than the light atoms, like hydrogen.) There's one obvious problem with all this. The absence of a compositional gradient would seem to suggest that all the planets should form with closely similar compositions. If the 'building material' in the inner solar system is the same as that which is found farther out, why is the Earth so different in composition from Jupiter? The reason they do not is a direct consequence of the temperature gradient. To understand this, let's start with a simple everyday analogy. On a sunny day, look up into the sky at the fluffy individual clouds floating above you. Ask yourself the following rather deep question: "Why are there clouds 'up there' but none here at ground level?" Your first thought might be that there is more water vapour high in the atmosphere than here at ground level, but that's not the case. In general the humidity at low altitudes can be just as high as it is farther up, yet even on very humid summer days we don't see clouds at ground level. So that can't be the reason. No, the real reason is that it is cool enough up there that little droplets of water can condense and form large clouds. Here at ground level, we see this phenomenon only occasionally, when the humidity is very high and the temperature is just right. Under those circumstances, fog or mist can form -- we are then quite literally 'inside a cloud.' More often, those conditions are not met, and the clouds float high above us. Similar considerations apply in in the early solar system. In the cooler outer parts, the temperature is low enough that essentially everything condenses -- even the light elements like hydrogen can condense into molecules, small particles and droplets. I should stress, however, that the material gets 'all mixed up.' You will not, for instance, get droplets of liquid hydrogen in one place, droplets of liquid nitrogen in another, etc., all independently. Instead, various atoms combine into many of the common chemical compounds, like water (H2O), methane (CH4), ammonia (NH3), and so forth. Since the original material is about two-thirds hydrogen and one-third helium, with only bits of everything else, your expectation would be that any planet which eventually forms far out in the solar system will have this kind of composition. This is why Jupiter is like the sun in composition. It also explains the great masses and sizes of the outer planets: all the gas which is present condenses, and since there is quite a lot of it, a big, bulky planet results. The material of which it is made, however, implies that it will be largely gaseous in structure and of low density. Closer to the sun, where it is much hotter, not everything can condense in the swirling nebula. Consider first the so-called volatile elements and compounds -- the substances like hydrogen, water vapour, and so on -- which boil off even at quite low temperatures. In the inner solar system, such substances stay completely gaseous in the same way that oxygen in the Earth's atmosphere does not form a liquid at room temperature. By contrast, the so-called refractory elements can condense (freeze). As their atoms and molecules collide, they stick together, and neither the random jiggling about of the constituent atoms nor occasional collisions from other particles are energetic enough to break them apart again: the chemical bonds are too strong. Near the hot sun, therefore, small grains (not necessarily liquid droplets) of such materials condense, consisting of things like metal oxides, alloys of nickel and iron, and so forth. They quickly grow to the size of pebbles. Once again, though, it is wrong to think of these species as forming a whole bunch of grains of iron in one place, plus a whole bunch of grains of aluminum oxide somewhere else, and so on. In general there will be a mixture of species in a given `pebble', so that you will see a very complex composition, just as you do if you examine a sample of granite or other Earth rock. A simple diagram on page 232 of the text shows the sorts of species that condense at different temperatures. The important point is that out where Jupiter eventually comes into existence, everything condenses; closer in, where Mercury will be found, only the heavier elements do. Please note that the difference in composition is not caused by the fact that heavy elements are more abundant near the sun. In fact, as I have noted and stressed, the mixture of gases was the same throughout the whole nebula at the time of formation. It is simply that the light gases don't condense at the high temperatures which prevail in the inner parts of the solar system. Since they never get locked up into grains, they never accumulate into planets by the process described below. A repeat warning: It is often thought by students, quite wrongly, that the heavier elements `sink towards the sun' and are therefore extra abundant there, giving rise to dense planets like Mercury. But this is not right. An obvious counter to this thought is to recognize that the sun itself is mostly hydrogen and helium, with only traces of heavy elements! Clearly the lighter gases were present everywhere when the solar system was young. (The sun retained these light gases because of its enormous gravity. The inner planets could not do this, and formed in a slow accumulation of small dense pieces made of heavier elements.) If you are clever, you will see that there is still a problem with this model. I am telling you that there was originally lots of hydrogen and helium in the inner parts of the solar system, swirling around in orbit along with the dense pebbles. Then I tell you that these light gases did not participate in the formation of the pebbles and the accumulation into the innermost planets, but also that the swirling (sideways) motion of the gases means that they could not fall into the sun. Where did they go? There are certainly no gases there now! -- the planets move through essentially empty space. We will see the answer to this important question in a bit. Our model certainly has to explain away this difficulty if it is to be trusted!

After the Pebbles? Planetesimals and Protoplanets.

Here's a very quick point-form summary of the processes described in more detail in your text (Chapter 9): The originally-distended nebula contracts and flattens out as it swirls. The composition remains uniform throughout. The central body -- the young sun -- becomes radiantly hot. Since the contraction brings the atoms much closer together, there are many collisions between them, and (depending on the temperature) we get the condensation of various kinds of small droplets, grains, and pebbles. What was a purely gaseous disk has now changed into a great number of small particles orbiting the sun, with a composition which depends on distance, plus (in the inner regions) uncondensed gases of the volatile elements like hydrogen and helium. Because of the original motion of the nebula, these pebbles are now moving in the same direction, more or less -- that is, they are orbiting the sun in the same sense, rather like cars on a racetrack. As a result, when two pebbles collide it is not generally like a head-on crash. Instead, they typically meet in gentle fashion at moderate speed, and can wind up sticking together because of chemical bonding and (as the various lumps grow) the increasing gravitation of the object. In this manner, the small pebbles accumulate into larger lumps - stones, boulders, and (eventually) planetesimals - literally `small planets' - about 10-100 km across, still numbering in the trillions. The process does not stop there. These bigger objects, although fewer in total number, still suffer collisions and accumulate into yet larger objects. These yet bigger objects are called protoplanets. I recognize that these names may seem a little arbitrary to you! How much does a 100-km planetesimal need to grow before it can be called a protoplanet? In a way, it seems like a fussy semantic distinction, but there is a useful way to look at it. When we have trillions of planetesimals, it is not possible to distinguish any one from the others in a fundamental way -- they are all very much alike. But after some time, there will be one which grows at the expense of the others and is identifiably the chunk which will be the planet. The reason for its growth is that its increasing gravitational influence provides what a physicist would call positive feedback: nearby planetesimals which would ordinarily drift past it will instead have their orbits significantly deflected. They fall in towards the lump and hit it, adding to the accumulated amount. This in turn increases the gravitational influence, and the process accelerates. Eventually, a few large planets result. On page 234 of the text, you can see the results of some computer simulations which demonstrate this process. The simulations are not perfect, of course. It is simply not possible to mimic the behaviour of trillions of orbiting pebbles, nor to accommodate the broad range of physical properties they would have. But the results are suggestive. We see that a vast cloud of orbiting planetesimals fairly quickly turn into just a handful of biggish planets. (Modern computers permit ever more realistic simulations of this sort.) I said that this happens fairly quickly. The analytic calculations suggest a time of about 100 million years, which may strike you as rather long! But recall that the solar system has an age of about 4.6 billion years, so that the formation process is a couple of percent of the total age. Here is an analogy: from conception to birth, a baby develops for nine months. Since the average human lifespan might be 75 years, that means that we spend about one percent of our lives in the formative process preceding birth. The solar system is not so very different.

Where Does the Leftover Gas Go? The Magic Broom.

As I told you above, the inner planets form in regions where little of the lighter elements condense, and so they are largely lacking in hydrogen and helium. (Of course, the Earth has some hydrogen on it, in the water which we find in the biosphere. But the total amount is very small.) What happened to the leftover gases? The answer is that we believe they were "swept out" of the solar system towards the end of the formation of the planetary system. The agency that does this is not completely understood, so it has earned the somewhat derisive term "the magic broom," but this is a little unfair because there is some strong evidence we can point to. For instance: the present sun has what is known as a "solar wind," a continuous outflow of charged particles (mostly electrons) which stream out through the solar system at a velocity of several hundred kilometers per second. Indeed, when there is a flare or eruption on the sun, the solar wind increases, and the particles hitting the upper parts of the Earth's atmosphere give rise to impressive displays of Northern Lights. there is a class of stars called T Tauri stars which are believed to be very similar to how the sun would have looked at the time of its formation. It has been determined that these stars have very strong winds, for reasons that are not completely understood. Something in the early life of such stars -- the "settling down" of the star as it establishes its nuclear reactions and so forth -- causes it briefly to behave in this fashion. The important point is that such winds are amply strong enough to drive any remaining gas out of the solar system in pretty short order. it can also be demonstrated that the atmospheres we now find around the rocky inner planets are almost certainly not what they were when the planets first formed. (The evidence comes from a study of the relative abundances of various isotopes of inert gases like argon. One might expect those relative abundances to be similar to what we see in the sun, but they are not.) The inference is that the atmospheres of the inner planets, including that of the Earth, were completely swept off at some early stage in the history of the solar system. The fact that they have atmospheres at all now is a result of the "outgassing" of the planets -- in particular, the pumping out of volatile substances by volcanoes. For instance, the water now found on the Earth would originally have condensed into the first grains and pebbles in the form of hydrates (complex chemicals which include water). The early Earth had sufficient gravity to hold onto some gases in its original atmosphere, but they would have been swept off by the magic broom. However, the Earth's active geology then led to considerable outgassing and the production of a secondary atmosphere (which has subsequently been changed even more by the appearance of life forms and so on). For all of these reasons, we believe that the unused gases in the inner parts of the solar system were swept out into space. The mechanism, as I have noted, is not absolutely clear, although important evidence continues to be found and understanding to develop. One very important point to note is that the solar wind, even in its enhanced ``Magic Broom'' phase, would be much too feeble to push big things around. Although it would sweep a distended gas out of the Solar System, it would have absolutely no effect on the planets and asteroids in their established orbits. (If you turn on a ceiling fan in the kitchen, it will get rid of the smoke from your burnt piece of toast, but it does not blow the pots and pans out of the room!)

Some Final Predictions.

If this general theory is correct, then there is one really obvious prediction. At the earliest times in the solar system, there must have been very large numbers of planetesimals orbiting around and colliding with the growing protoplanets. Since the planetesimals get "used up" in forming the planets, their numbers will drop. Consequently, we should find that the bombardment rate (i.e. the numbers of collisions) should have been very high early on, but fallen off fairly precipitously as time passed. This is not something we can test directly on the Earth, because our atmosphere and active geology has long since obliterated almost all traces of what happened in the early days. But "fossil" objects like the moon, which have no active geology, are ideal for this purpose. Indeed, part of the motivation for the lunar landings in the 60's and 70's was to hunt for so-called `Genesis rocks' - to bring back samples which could be tested and have their ages determined, so that we could test the hypothesis that the most heavily cratered regions of the lunar surface are indeed remnants of that heavy bombardment shortly after the Solar System formed. (The smoother, flatter regions of the moon, the maria, were formed later by the upwelling of large amounts of lava which spread out over the lunar surface and obliterated traces of the ancient heavy bombardment.) We have visited the moon and measured the ages of rocks in various locations, and we find that the prediction is indeed borne out. The moon was clobbered by many large chunks early in its life, but the rate of bombardment then fell rapidly to a much lower level, just as the model would predict. There is a second understanding which the model allows us: we now realise that, late in the formation process, there must have been some pretty large lumps moving around in the solar system. Not all of these would have been orbiting in completely parallel paths, especially since the directions of motion can be altered by the gravitational tugs of other objects; thus there may occasionally have been really vigorous collisions between enormous fast-moving lumps of rock. This may explain, among other things: why Uranus is tipped on its side. Its spin axis lies almost exactly in the plane of the Solar System (see page 344 of your text), an effect which may have been caused by a collision between the newly-formed Uranus and some large chunk which came roaring in and hit it off-centre; how the Earth's moon came to be. The present understanding of this is described on pages 238-240 of your text, along with a dramatic illustration showing the Earth being clobbered by a Mars-sized chunk early in its life.

Other Solar Systems?

If our theory is correct, the formation of planets seems a routine and almost inescapable part of star formation. In other words, most of the stars in the sky might be expected to have planets in orbit around them. Until recently, testing this was not easy: the search for other planets is in fact very difficult. If you were to look at the sun from another nearby star -- Sirius, for example -- you would not be able to detect Jupiter in any obvious way. (We will explore some of these questions when we discuss the search for life in the universe.) Nonetheless, we have had some important successes, of two kinds: 1 We have identified disks of material surrounding a few nearby stars, disks that we think are comparable to the early solar nebula. The figures on page 230 of your text shows images of the disks around the stars Beta Pictoris and AB Aurigae. 2 More recently, we have actually succeeded in detecting planets around dozens of the nearer stars -- not, I hasten to add, by actually seeing them, but rather by deducing the presence of a planet to explain why the target star is wobbling back and forth in space as it and the planet orbit their common center of mass (like the two ends of a thrown baton). Since a star is much more massive than any planet orbiting it, the star's motion is very small, but can now just be measured with modern instruments; moreover, the changes can be tracked over many months or years. This is well described on pages 243-248. If the data are good enough, one can actually sometimes deduce the presence of more than one planet (one of the systems seems to have at least three planets) but more typically only the dominant one, the counterpart of our own Jupiter around the Sun, can be incontestably demonstrated to exist. One of the most important recent breakthroughs in modern astronomy is that the data are now of sufficient quality, and cover a long enough timespan, that these demanding analyses can be made. This is a field of research which is progressing at an enormous rate, and the figure presented on page 246 of your textbook is already out of date. But the critical point is that these detections really put an end to the catastrophic hypothesis. Something much more routine must be generating planets in such abundance -- something like the nebular model we have been discussing. Previous chapter:Next chapter

0: Physics 015: The Course Notes, Fall 2004 1: Opening Remarks: Setting the Scene. 2: The Science of Astronomy: 3: The Importance of Scale: A First Conservation Law. 4: The Dominance of Gravity. 5: Looking Up: 6: The Seasons: 7: The Spin of the Earth: Another Conservation Law. 8: The Earth: Shape, Size, and State of Rotation. 9: The Moon: Shape, Size, Nature. 10: The Relative Distances and Sizes of the Sun and Moon: 11: Further Considerations: Planets and Stars. 12: The Moving Earth: 13: Stellar Parallax: The Astronomical Chicken 14: Greek Cosmology: 15: Stonehenge: 16: The Pyramids: 17: Copernicus Suggests a Heliocentric Cosmology: 18: Tycho Brahe, the Master Observer: 19: Kepler the Mystic. 20: Galileo Provides the Proof: 21: Light: Introductory Remarks. 22: Light as a Wave: 23: Light as Particles. 24: Full Spectrum of Light: 25: Interpreting the Emitted Light: 26: Kirchhoff's Laws and Stellar Spectra. 27: Understanding Kirchhoff's Laws. 28: The Doppler Effect: 29: Astronomical Telescopes: 30: The Great Observatories: 31: Making the Most of Optical Astronomy: 32: Adaptive Optics: Beating the Sky. 33: Radio Astronomy: 34: Observing at Other Wavelengths: 35: Isaac Newton's Physics: 36: Newtonian Gravity Explains It All: 37: Weight: 38: The Success of Newtonian Gravity: 39: The Ultimate Failure of Newtonian Gravity: 40: Tsunamis and Tides: 41: The Organization of the Solar System: 42: Solar System Formation: 43: The Age of the Solar System: 44: Planetary Structure: The Earth. 45: Solar System Leftovers: 46: The Vulnerability of the Earth: 47: Venus: 48: Mars: 49: The Search for Martian Life: 50: Physics 015 - Parallel Readings.

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Mystery destination!

(Friday, 28 January, 2022.)